Unfortunately, severe problems connected with the retrieval and analysis of DNA from ancient organisms (like the scarcity of intact molecules) are further aggravated in the case of ancient humans. This is because of the great risk of contamination with abundant DNA from modern humans. Humans, then, are involved at all steps, from excavation to laboratory analyses. This means that many previous results have subsequently been disputed as attributed to the presence of contaminant DNA, and some researchers even claim that it is impossible to obtain reliable results with ancient human DNA

The limits of genetic research also plays a role. DNA can give a probability of being related but it is not an infallible research field

Plus genetic research cannot shed any light on interpersonal relationships or how societies behaved when they were alive. Now a researcher may find similar DNA with Homo Sapiens in a few supposed Neanderthal but that does not indicate that ALL Neanderthals intermingled with Homo Sapiens.

Nor does it prove that the Neanderthal were a sub-species and if it did then that would open up the Chinese, the Hispanic, the Black to charges that they are merely sub-speices of white Homo Sapiens and be used to support racism.

Without written material from the time period that actually can be proven to be accurate, scientists cannot construct a viable civilization for the Neanderthal nor even say there were actually a sub-species.

There were different tribes of man; we survived and they didn't. Why not add back some genetic diversity. Get a population of Neanderthals going and then have sex with them and make some homo-neander half breeds.

Humans have already interbred with Neanderthals, probably including some of your ancestors.